CN114371379A - A method and system for measuring space charge injection threshold electric field - Google Patents

Abstract

The invention relates to a method and a system for measuring a space charge injection threshold electric field, comprising the following steps: obtaining a sample subjected to metallization treatment, and externally connecting an initial direct current electric field at two ends of the sample; applying laser pulse to the metallized side of the sample, and collecting the response current generated by the sample under the action of the laser pulse; and calculating the electric field intensity near the surface layer in the sample according to the response current, if the calculated surface layer electric field intensity is equal to the external electric field intensity, increasing the external direct current electric field, and continuing to calculate the surface layer electric field intensity of the sample, otherwise, injecting the external electric field serving as the space charge of the sample into the threshold electric field. Compared with the prior art, the method utilizes an instantaneous thermal disturbance method, calculates the electric field distribution near the surface layer in the sample according to the thermal response current formed under the thermal disturbance, compares the calculated surface layer electric field distribution with the external uniform electric field, and considers that the external electric field strength at the moment reaches the space charge injection threshold electric field of the sample when the external electric field deviates from the calculated surface layer electric field distribution.

Description

A method and system for measuring space charge injection threshold electric field

technical field

The present invention relates to parameter measurement of dielectric materials, in particular to a method and system for measuring the space charge injection threshold electric field of insulating materials.

Background technique

Polymer dielectric materials are widely used as functional materials in microelectronics, electrical insulation and energy storage capacitors due to their excellent mechanical properties, fatigue resistance and electrical insulation. Space charge generally refers to a positive or negative net charge that exists in a local space. Dielectric materials accumulate space charges when they are subjected to high electric fields or placed in an environment irradiated by charged particles. The long-term performance of polymer dielectric materials under the action of an electric field is very important. The space charge injection threshold is one of the most important parameters. The existence of this threshold will have a considerable impact on the design of the insulating system. The measurement of the space charge injection threshold electric field has been a very important topic.

The existing measurement method is to use the electroacoustic pulse method and the pressure wave method to measure the threshold electric field of space charge injection in a medium with a thickness of several hundreds of micrometers to several millimeters. According to the measurement principles of these two methods, the test waveforms of the electroacoustic pulse method and the pressure wave method contain the induced charge peak of the electrode, and the width of the induced charge peak is usually more than 20-30 μm, which will cause the injected charge signal to be submerged in the In the induced charge peak, it is impossible to judge the initial injection of space charge. The method reported so far is to use the applied electric field strength when the injected charge is separated from the electrode peak to a distinguishable distance as the judgment of the threshold electric field of charge injection. At this time, there is not only the accumulation of injected charges near the electrode interface, but some of the injected charges have been By migrating away from the electrode interface, it reaches deeper parts of the sample. Therefore, using such a standard as the threshold electric field of space charge injection will bring obvious errors, and the main reason for the inaccuracy of the threshold electric field of space charge injection measured by the electroacoustic pulse method and the pressure wave method is the insufficient spatial resolution of the measurement.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method and system for measuring the threshold electric field of space charge injection in order to overcome the above-mentioned defects of the prior art.

The object of the present invention can be realized through the following technical solutions:

A method for measuring a space charge injection threshold electric field, comprising the following steps:

S1. Obtain a metallized sheet sample, and connect an initial DC electric field at both ends of the sample;

S2. Apply a laser pulse to the metallized side of the sample, and collect the response current generated by the sample under the action of the laser pulse;

S3. Calculate the electric field intensity near the surface layer inside the sample according to the response current. If the calculated surface electric field intensity is equal to the external electric field intensity, increase the external DC electric field at both ends of the sample, and perform step S2, otherwise, the calculated The surface electric field intensity deviates from the external electric field intensity, and the external DC electric field at this time is injected into the threshold electric field as the space charge of the sample.

Further, calculating the electric field intensity in the sample according to the response current is as follows:

The response current is described using the Fredholm integral equation of the first kind:

Among them, I(t) represents the collected response current, r represents the incident spot radius of the laser pulse applied to the sample, d represents the thickness of the sample, x represents the spatial position along the thickness direction of the sample, t represents the time, and g (x) represents the electric field distribution correlation function, ΔT(x, t) represents the temperature increment change inside the sample, and:

g(x)=ε ₀ ε _r (α _ε -α _x )E(x)

E(x) represents the electric field distribution inside the sample, ε ₀ , ε _r represent the vacuum permittivity of the sample and the relative permittivity of the sample, respectively, α _ε , α _x represent the relative permittivity of the sample, respectively temperature coefficient and thermal expansion coefficient;

The calculation model of the incremental temperature change ΔT(x, t) inside the sample is as follows:

The initial conditions are:

△T(x, 0)| _t=0 =0

The boundary conditions are:

The heat conduction equation is:

Among them, D represents the thermal diffusivity of the sample, k represents the thermal conductivity of the sample, η represents the absorption rate of the surface of the sample to the incident laser pulse energy, α represents the amplitude of the laser pulse, and β represents the width of the laser pulse;

According to the initial conditions and boundary conditions, combined with the heat conduction equation, the temperature increment change ΔT(x, t) inside the sample is obtained, and the calculated ΔT(x, t) and the collected I(t) are substituted into the first type The Fredholm integral equation obtains the electric field distribution correlation function g(x) inside the sample, and then calculates the electric field distribution E(x).

并以满足r/x≥Kp作为条件将得到的频域信号分为高频段和低频段，ω为信号频率，Kp为预设置的分段阈值，根据高频段的频段长度确定采集时间。Further, the laser pulse is used as a thermal disturbance in the process of heat conduction inside the sample, and the disturbance gradually changes from high frequency to low frequency. The side that receives the laser pulse is used as the test surface of the sample, and the frequency is disturbed in the area close to the test surface inside the sample. is high frequency, this area is an effective test area, and the collection time of the response current is determined according to the thickness of the effective test area, specifically: converting the collected response current from the time-domain signal I(t) to the frequency-domain signal I (ω), according to the perturbation frequency and spatial position transformation relationship

And satisfy r/x≥Kp as the condition to divide the obtained frequency domain signal into high frequency band and low frequency band, ω is the signal frequency, Kp is the preset segmentation threshold, and the acquisition time is determined according to the frequency band length of the high frequency band.

Further, the acquisition time is determined according to the thickness of the effective test area, the response current I(t) is collected, and the incremental temperature change ΔT(x, t), substitute I(t) and ΔT(x, t) into the Fredholm integral equation of the first kind, and use the Honzenoff algorithm to calculate the electric field distribution correlation function g( x), and then calculate the electric field distribution E(x) in the effective test area.

Further, the incident spot diameter of the laser pulse applied to the sample is more than 2 orders of magnitude higher than the thickness of the effective test area of the sample, and the thickness of the sample is more than one order of magnitude larger than the thickness of the effective test area.

Further, in step S3, the external DC electric field at both ends of the sample is increased according to a preset step size.

Further, in step S1, the thin sheet sample is a sheet structure sample with single-sided or double-sided metallization.

A measurement system for a space charge injection threshold electric field, comprising:

Holder for single- or double-sided metallized sheet specimens,

The voltage unit is used to connect an electric field at both ends of the sample, and the voltage unit is provided with an electric field intensity regulation module;

A laser unit for applying laser pulses to the metallized side of the specimen;

The acquisition unit is used to collect the response current generated by the sample under the action of the laser pulse;

The control unit is connected in communication with the voltage unit, the laser unit and the acquisition unit, and calculates the electric field intensity near the surface layer inside the sample according to the response current. If the calculated surface electric field intensity is equal to the electric field intensity outside the sample, increase the two The DC electric field externally connected to the end of the sample continues to calculate the electric field strength of the near-surface layer inside the sample, otherwise, the external DC electric field at this time is output as the space charge injection threshold electric field of the sample.

Further, calculating the electric field intensity in the sample according to the response current is as follows:

The response current is described using the Fredholm integral equation of the first kind:

Among them, I(t) represents the collected response current, r represents the incident spot radius of the laser pulse applied to the sample, d represents the thickness of the sample, x represents the spatial position along the thickness direction of the sample, t represents the time, and g (x) represents the electric field distribution correlation function, ΔT(x, t) represents the temperature increment change inside the sample, and:

g(x)=ε ₀ ε _r (α _ε -α _x )E(x)

E(x) represents the electric field distribution inside the sample, ε ₀ , ε _r represent the vacuum permittivity of the sample and the relative permittivity of the sample, respectively, α _ε , α _x represent the relative permittivity of the sample, respectively temperature coefficient and thermal expansion coefficient;

The calculation model of the incremental temperature change ΔT(x, t) inside the sample is as follows:

The initial conditions are:

△T(x,0)| _t=0 =0

The boundary conditions are:

The heat conduction equation is:

Among them, D represents the thermal diffusivity of the sample, k represents the thermal conductivity of the sample, η represents the absorption rate of the surface of the sample to the incident laser pulse energy, α represents the amplitude of the laser pulse, and β represents the width of the laser pulse;

According to the initial conditions and boundary conditions, combined with the heat conduction equation, the temperature increment change ΔT(x, t) inside the sample is obtained, and the calculated ΔT(x, t) and the collected I(t) are substituted into the first type The Fredholm integral equation obtains the electric field distribution correlation function g(x) inside the sample, and then calculates the electric field distribution E(x).

并以满足r/x≥Kp作为条件将得到的频域信号分为高频段和低频段，ω为信号频率，Kp为预设置的分段阈值，根据高频段的频段长度确定采集时间。Further, the laser pulse is used as a thermal disturbance in the process of heat conduction inside the sample, and the disturbance gradually changes from high frequency to low frequency. The side that receives the laser pulse is used as the test surface of the sample, and the frequency is disturbed in the area close to the test surface inside the sample. is high frequency, this area is an effective test area, and the collection time of the response current is determined according to the thickness of the effective test area, specifically: converting the collected response current from the time-domain signal I(t) to the frequency-domain signal I (ω), according to the perturbation frequency and spatial position transformation relationship

And satisfy r/x≥Kp as the condition to divide the obtained frequency domain signal into high frequency band and low frequency band, ω is the signal frequency, Kp is the preset segmentation threshold, and the acquisition time is determined according to the frequency band length of the high frequency band.

Compared with the prior art, the present invention has the following beneficial effects:

(1) Using the instantaneous thermal disturbance method, a laser pulse is applied to the sample with an external uniform electric field, and the electric field distribution in the sample is calculated according to the thermal response current formed under the thermal disturbance, and the calculated electric field distribution is compared with the external uniform electric field. , when there is a deviation between the external uniform electric field and the calculated electric field distribution, it is considered that the space charge injection threshold electric field of the sample is reached.

(2) By calculating the instantaneous thermal response current through the heat transfer model, the space charge injection threshold electric field of the polymer film with a thickness of several hundreds of microns can be measured, and the measurement deviation caused by the spatial resolution limitation of the electroacoustic pulse method and the pressure wave method can be overcome. , the sub-micron spatial resolution of the measurement of the space charge or electric field distribution on the surface of the sample can be obtained, thereby realizing the accurate measurement of the electric field at the threshold of space charge injection.

(3) The method is simple, the operation is convenient, the measurement speed is fast, the sample is not damaged, and the space charge threshold electric field of the medium sample can be determined effectively and accurately.

Description of drawings

Fig. 1 is the schematic diagram of sample receiving laser pulse and external circuit;

Figure 2 shows the electric field distribution and space charge distribution calculated by injecting charges near the surface inside the 300 μm PP film.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and provides a detailed implementation manner and a specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

In the drawings, structurally identical components are denoted by the same numerals, and structurally or functionally similar components are denoted by like numerals throughout. The size and thickness of each component shown in the drawings are arbitrarily shown, and the present invention does not limit the size and thickness of each component. Parts in the drawings have been appropriately exaggerated in some places for clarity of illustration.

Example 1:

A method for measuring a space charge injection threshold electric field, comprising the following steps:

S1. Obtain a single-sided or double-sided metallized sheet sample, and connect an initial DC electric field at both ends of the sample;

S2. Apply a laser pulse to the metallized side of the sample, and collect the response current generated by the sample under the action of the laser pulse;

S3. Calculate the electric field intensity near the surface layer inside the sample according to the response current. If the calculated surface electric field intensity is equal to the external electric field intensity, increase the external DC electric field at both ends of the sample, and perform step S2, otherwise, it is considered that the calculation is obtained. The surface electric field strength deviates from the external electric field strength, and the external DC electric field at this time is injected into the threshold electric field as the space charge of the sample.

After analysis, the inventor found that the spatial resolution of the electroacoustic pulse method and the pressure wave method is proportional to the speed of sound. Since the speed of sound usually has a speed of several thousand meters per second in the medium, this is the electroacoustic pulse method based on the measurement principle of the speed of sound. It is one of the main reasons why it is difficult to obtain micron-scale resolution with the pressure wave method. Therefore, considering that the heat conduction is much slower than the speed of sound, the application integrates the basic theory of heat transfer to establish a heat transfer model, through an external DC electric field, there is a uniformly distributed electric field inside the sample of the thin sheet structure, and a short pulse laser is used to generate an instantaneous transient on the surface of the sample. Thermal disturbance, calculate and analyze the instantaneous thermal response current generated by the sample under thermal disturbance, and obtain sub-micron spatial resolution for the measurement of the space charge or electric field distribution on the surface of the sample, so as to achieve accurate measurement of the space charge injection threshold electric field.

In step S3, calculating the electric field intensity in the sample according to the response current is as follows:

The response current is described using the Fredholm integral equation of the first kind:

Among them, I(t) represents the collected response current, r represents the incident spot radius of the laser pulse applied to the sample, d represents the thickness of the sample, x represents the spatial position along the thickness direction of the sample, t represents the time, and g (x) represents the electric field distribution correlation function, ΔT(x, t) represents the temperature increment change inside the sample, and:

g(x)=ε ₀ ε _r (α _ε -α _x )E(x)

E(x) represents the electric field distribution inside the sample, ε ₀ , ε _r represent the vacuum permittivity of the sample and the relative permittivity of the sample, respectively, α _ε , α _x represent the relative permittivity of the sample, respectively temperature coefficient and thermal expansion coefficient;

For dielectric samples with a thickness of hundreds of microns to millimeters, under the continuous action of an externally applied DC electric field, when the surface of the sample is disturbed by a short-time laser pulse, part of the incident laser energy is absorbed by the sample to form an instantaneous thermal disturbance. Considering that the effective thermal disturbance range formed by the laser pulse is only tens of microns, if the diameter of the incident laser spot is in the order of millimeters, the heat propagation in the dielectric sample can be approximately described by a one-dimensional heat conduction equation. The calculation model of the incremental temperature change ΔT(x, t) inside the sample is as follows:

The initial conditions are:

△T(x, 0)| _t=0 =0

The boundary conditions are:

The heat conduction equation is:

Among them, D represents the thermal diffusivity of the sample, k represents the thermal conductivity of the sample, η represents the absorption rate of the surface of the sample to the incident laser pulse energy, α represents the amplitude of the laser pulse, and β represents the width of the laser pulse;

According to the initial conditions and boundary conditions, combined with the heat conduction equation, the temperature increment change ΔT(x, t) inside the sample is obtained, and the calculated ΔT(x, t) and the collected I(t) are substituted into the first type The Fredholm integral equation obtains the electric field distribution correlation function g(x) inside the sample, and then calculates the electric field distribution E(x).

The diameter of the incident spot of the laser pulse applied to the sample is more than 2 orders of magnitude higher than the thickness of the sample. Considering that the sample is a relatively thick sheet relative to the spot diameter, the disturbance heat will gradually show a two-dimensional shape after entering the sample. The way heat is conducted, therefore, the thermally responsive current cannot be directly described by Equation 1.

The study found that the incident instantaneous thermal disturbance has dispersion characteristics in the conduction process of the dielectric sample. The disturbance of the incident thermal disturbance to the sample gradually changes from high frequency to low frequency during the heat conduction process, and the corresponding response current signal also changes from high frequency to low frequency. for low frequency. The side that receives the laser pulse is the test surface of the sample, and the disturbance frequency is high frequency in the area close to the test surface inside the sample, and this area is the effective test area. As shown in Figure 1, generally speaking, the effective thermal disturbance range formed by laser pulses is only tens of microns, and the dielectric sample used in this application is a thin sheet structure. Therefore, based on experience and some pre-experiments, the effective test area can be basically determined. The thickness of , that is, the effective test area inside the sample near the test surface. In the effective test area, the heat conduction is still mainly characterized by one-dimensional conduction. At this time, Equation 1 still applies. In the farther invalid test area, the formula 1 is no longer applicable due to the two-dimensional conduction mode of the disturbance heat.

The lowest frequency of the frequency domain signal is related to the signal acquisition cutoff time. The shorter the acquisition time, the higher the minimum frequency of the frequency domain signal, so the acquisition cut-off time can be reasonably reduced, so that there is no low-frequency signal that does not conform to one-dimensional heat conduction in the acquired response current.

In order to determine the sampling time, a signal acquisition can be performed first to obtain the response current signal I(t), the temperature increment distribution ΔT(x, t) can be obtained by calculation, and the response current signal can be converted from the time domain signal I(t) to the frequency signal. Domain signal I(ω), specifically:

Substitute Equation 1 into the Fourier transform definition, swap the order of integration, and integrate by parts:

Among them, I(ω) represents the response current signal in the frequency domain, ω represents the frequency point, πr ² represents the laser irradiation area of the sample, and then substitute formula 2 into the above formula to obtain the frequency domain signal I(ω):

where the Fourier coefficients g _n of g(x) are given by:

Among them, T ₀ =ηq/(cρAd), T ₀ represents the thermal equilibrium temperature inside the sample, q represents the laser pulse energy applied to the sample, c is the specific heat capacity of the sample, ρ is the density of the sample, A=πr ² , τ represents the heat transfer time coefficient.

并以满足r/x≥Kp作为条件将得到的频域信号分为高频段和低频段，本实施例中Kp取50，剔除低频段的数据，保留高频段的数据，在高频段，热传导仍以一维传导为主要特征，根据高频段的频段长度确定采集时间。Set the segmentation threshold Kp according to the thickness of the effective test area, and transform the relationship according to the disturbance frequency and spatial position

And satisfy the condition of r/x≥Kp to divide the obtained frequency domain signal into high frequency band and low frequency band. In this embodiment, Kp is taken as 50, the data in the low frequency band is excluded, and the data in the high frequency band is retained. In the high frequency band, the heat conduction is still With one-dimensional conduction as the main feature, the acquisition time is determined according to the frequency band length of the high frequency band.

In this way, the acquisition time is determined according to the thickness of the effective test area, the response current I(t) is collected, and the incremental temperature change ΔT(x, t) inside the sample is calculated according to the initial conditions and the heat conduction equation of the initial conditions by numerical calculation method. ), substituting I(t) and ΔT(x, t) into the Fredholm integral equation of the first kind, and using the Honzenoff algorithm to calculate the electric field distribution correlation function g(x) in the effective test area inside the sample ), and then calculate the electric field distribution E(x) in the effective test area.

After the preparation is completed, the space charge injection threshold electric field measurement of the sample can be started. The basic experimental steps are as follows:

1) Metallize the surface of one or both sides of the sample;

2) As shown in Figure 1, the surface of the sample with the metallized layer is used as the test surface, the metallized electrode of the test surface is grounded, and at the same time, it is used as a pulsed laser radiation target to receive laser pulses;

3) As shown in Figure 1, for the other side of the sample, connect this side to a positive or negative DC voltage as needed, that is, HVDC in Figure 1, and connect a signal coupling capacitor to the electrode on this side;

4) Apply an initial DC electric field of 1kV/mm to the sample, and the size of the initial DC electric field can be adjusted according to actual needs;

5) According to the condition of the sample, after the applied voltage is stable for 1-10 minutes, the metallized electrode of the test surface is irradiated with pulsed laser continuously for multiple times;

6) The average response current of the sample to the laser pulse irradiation is collected by a digital oscilloscope through the signal coupling capacitor;

7) According to the calculation principle mentioned above, analyze the response current, and calculate the electric field strength of the effective test area;

8) When the electric field strength of the effective test area obtained by calculation is equal to the applied uniform electric field strength, it is considered that there is no space charge injection, and the space charge injection threshold electric field of the sample has not been reached, and the applied electric field is gradually increased according to the step size of 1kV/mm. Repeat steps 5)-8) until the calculated electric field intensity deviates from the applied uniform electric field in the effective test area. At this time, the corresponding applied DC electric field intensity is the space charge injection threshold electric field of the sample, and the step size can be Adjust according to actual needs.

By setting the sampling time reasonably, it is ensured that the collected response current signal is a high-frequency signal, corresponding to the one-dimensional heat conduction of the heat in the effective area, so as to calculate the electric field distribution. Gradually increase the external electric field, and a certain deviation judgment standard can be set as required. When the electric field strength in the effective test area deviates from the external uniform electric field, it is considered that the space charge injection threshold electric field of the sample has been reached.

As shown in Figure 2, when injecting charges into a 300μm PP film in a 0-10μm space position, the instantaneous thermal disturbance method provided by this application is used. In Figure 2 (1) is the preset electric field distribution and the calculated electric field distribution, ( 2 ) in FIG. 2 shows the preset space charge distribution and the calculated space charge distribution. It can be seen that the calculated electric field distribution and space charge distribution can be well fitted to the preset electric field distribution and charge distribution, indicating that the measurement of the electric field distribution and electric field distribution on the surface of the sheet is completely feasible, and the measurement accuracy is high. .

In this application, the instantaneous thermal disturbance method is used to obtain the electric field distribution near the surface of the relatively thick sample. When there is a certain deviation between the calculated electric field intensity and the external electric field intensity, it is considered that space charge occurs and the space of the sample is reached. Charge injection threshold electric field. Compared with the pressure wave method and the electroacoustic pulse method, the present application has higher spatial resolution, can measure the possible lower space charge threshold electric field, and at the same time can observe the space charge injection near the test surface of the sample .

The present application provides a simple and effective method to measure the space charge injection threshold electric field of a polymer film with a thickness of several hundreds of microns, and overcomes the measurement deviation caused by the spatial resolution limitation of the electroacoustic pulse method and the pressure wave method. The measurement of the present application belongs to the transient measurement method, which is easy to operate, has a fast measurement speed, does not damage the sample, and can effectively and accurately determine the space charge threshold electric field of the dielectric sample.

Example 2:

A measurement system for a space charge injection threshold electric field, comprising:

Holder for placing single-sided or double-sided metallized sheet samples;

The voltage unit is used to connect an electric field at both ends of the sample, and the voltage unit is provided with an electric field intensity control module;

A laser unit for applying laser pulses to the metallized side of the specimen;

The acquisition unit is used to collect the response current generated by the sample under the action of the laser pulse;

The control unit is connected in communication with the voltage unit, the laser unit and the acquisition unit, and calculates the electric field intensity near the surface layer inside the sample according to the response current. If the calculated surface electric field intensity is equal to the electric field intensity outside the sample, increase the two The DC electric field externally connected to the end of the sample continues to calculate the electric field strength of the near-surface layer inside the sample, otherwise, the external DC electric field at this time is output as the space charge injection threshold electric field of the sample. In the control unit, the calculation process of obtaining the electric field strength of the inner near-surface layer of the sample according to the response current has been described in Embodiment 1, and will not be repeated here.

The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make many modifications and changes according to the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art through logical analysis, reasoning or limited experiments on the basis of the prior art according to the concept of the present invention shall fall within the protection scope determined by the claims.

Claims (10)

1. A method for measuring a space charge injection threshold electric field, comprising the steps of:

s1, obtaining a metallized slice sample, and externally connecting an initial direct current electric field at two ends of the sample;

s2, applying laser pulses to the metallized side of the sample, and collecting response current generated by the sample under the action of the laser pulses;

s3, calculating the electric field intensity near the surface layer in the sample according to the response current, if the calculated surface layer electric field intensity is equal to the external electric field intensity, increasing the direct current electric field externally connected at the two ends of the sample, and executing the step S2, otherwise, the calculated surface layer electric field intensity deviates from the external electric field intensity, and injecting the external direct current electric field into the threshold electric field as the space charge of the sample.

2. The method according to claim 1, wherein calculating the electric field strength in the sample based on the response current comprises:

the response current is described using a first class of Fredholm integral equations:

wherein i (T) represents the collected response current, r represents the incident spot radius of the laser pulse applied to the specimen, d represents the thickness of the specimen, x represents the spatial position in the thickness direction of the specimen, T represents time, g (x) represents the electric field distribution correlation function, Δ T (x, T) represents the incremental change in temperature inside the specimen, and:

g(x)＝ε₀ε_r(α_ε-α_x)E(x)

e (x) represents the electric field distribution, ε, in the sample₀、ε_rVacuum dielectric constant of respective samplesNumber and relative dielectric constant of the sample, alpha_ε、α_xA temperature coefficient and a thermal expansion coefficient respectively representing the relative dielectric constant of the sample;

the model for calculating the temperature increase change Δ T (x, T) inside the sample is as follows:

the initial conditions were:

ΔT(x,0)|_t＝0＝0

the boundary conditions are as follows:

the heat transfer equation is:

wherein D represents the thermal diffusivity of the sample, k represents the thermal conductivity of the sample, η represents the absorption rate of the sample surface to the energy of the incident laser pulse, α represents the amplitude of the laser pulse, and β represents the width of the laser pulse;

according to the initial condition and the boundary condition, combining a heat conduction equation to obtain the temperature increment change delta T (x, T) in the sample, substituting the delta T (x, T) obtained by calculation and the collected I (T) into a first class of Fredholm integral equation to obtain the electric field distribution correlation function g (x) in the sample, and further calculating to obtain the electric field distribution E (x).

3. The method according to claim 2, wherein the disturbance of the laser pulse gradually changes from a high frequency to a low frequency during the heat conduction inside the sample as a thermal disturbance, the side receiving the laser pulse is a test side of the sample, and the disturbance frequency is a high frequency in a region inside the sample close to the test sideThe region is an effective test region, and the acquisition time of the response current is determined according to the thickness of the effective test region, specifically: converting the collected response current from time domain signal I (t) into frequency domain signal I (omega), and transforming the relation according to the disturbance frequency and the space position

And dividing the obtained frequency domain signal into a high frequency band and a low frequency band by taking the condition that r/x is more than or equal to Kp as a condition, wherein omega is the signal frequency, Kp is a preset segmentation threshold, and the acquisition time is determined according to the frequency band length of the high frequency band.

4. The method for measuring the space charge injection threshold electric field according to claim 3, wherein the collecting time is determined according to the thickness of the effective test region, the response current I (T) is collected, the temperature increment change Δ T (x, T) inside the sample is obtained by numerical calculation according to the initial condition and the heat conduction equation of the initial condition, the I (T) and the Δ T (x, T) are substituted into the first class of Fredholm integral equation, the electric field distribution correlation function g (x) in the effective test region inside the sample is obtained by calculation through the Hongzhinov algorithm, and the electric field distribution E (x) in the effective test region is obtained by calculation.

5. The method according to claim 4, wherein the incident spot diameter of the laser pulse applied to the sample is 2 orders of magnitude or more higher than the effective test area thickness of the sample, and the sample thickness is more than one order of magnitude greater than the effective test area thickness.

6. The method for measuring the space charge injection threshold electric field according to claim 1, wherein in step S3, the dc electric field externally connected to the two ends of the sample is increased according to a preset step size.

7. The method according to claim 1, wherein in step S1, the sheet sample is a sheet structure sample with one or both sides metallized.

8. A space charge injection threshold electric field measurement system based on a space charge injection threshold electric field measurement method according to any one of claims 1 to 7, comprising:

the fixing frame is used for placing the metallized slice sample;

the voltage unit is used for externally connecting electric fields at two ends of the sample and is provided with an electric field intensity regulating and controlling module;

a laser unit for applying a laser pulse to a metallization side of a sample;

the acquisition unit is used for acquiring response current generated by the sample under the action of laser pulse;

and the control unit is in communication connection with the voltage unit, the laser unit and the acquisition unit, calculates the electric field intensity near the surface layer in the sample according to the response current, increases the external direct current electric fields at two ends of the sample if the calculated electric field intensity of the surface layer is equal to the external electric field intensity of the sample, continues to calculate the electric field intensity near the surface layer in the sample, and otherwise, outputs the external direct current electric field as the space charge injection threshold electric field of the sample.

9. The system for measuring a space charge injection threshold electric field according to claim 8, wherein the calculation of the electric field strength in the sample based on the response current is specifically:

the response current is described using a first class of Fredholm integral equations:

wherein i (T) represents the collected response current, r represents the incident spot radius of the laser pulse applied to the specimen, d represents the thickness of the specimen, x represents the spatial position in the thickness direction of the specimen, T represents time, g (x) represents the electric field distribution correlation function, Δ T (x, T) represents the incremental change in temperature inside the specimen, and:

g(x)＝ε₀ε_r(α_ε-α_x)E(x)

e (x) represents the electric field distribution, ε, in the sample₀、ε_rRespectively showing the vacuum dielectric constant of the sample and the relative dielectric constant, alpha, of the sample_ε、α_xA temperature coefficient and a thermal expansion coefficient respectively representing the relative dielectric constant of the sample;

the model for calculating the temperature increase change Δ T (x, T) inside the sample is as follows:

the initial conditions were:

ΔT(x,0)|_t＝0＝0

the boundary conditions are as follows:

the heat transfer equation is:

wherein D represents the thermal diffusivity of the sample, k represents the thermal conductivity of the sample, η represents the absorption rate of the sample surface to the energy of the incident laser pulse, α represents the amplitude of the laser pulse, and β represents the width of the laser pulse;

according to the initial condition and the boundary condition, combining a heat conduction equation to obtain the temperature increment change delta T (x, T) in the sample, substituting the delta T (x, T) obtained by calculation and the collected I (T) into a first class of Fredholm integral equation to obtain the electric field distribution correlation function g (x) in the sample, and further calculating to obtain the electric field distribution E (x).

10. A space charge according to claim 9The system for measuring the injection threshold electric field is characterized in that the disturbance of a laser pulse serving as thermal disturbance in the process of heat conduction in a sample is gradually changed from high frequency to low frequency, one surface receiving the laser pulse serves as a test surface of the sample, the disturbance frequency in an area close to the test surface in the sample is high frequency, the area is an effective test area, and the acquisition time of response current is determined according to the thickness of the effective test area, and specifically comprises the following steps: converting the collected response current from time domain signal I (t) into frequency domain signal I (omega), and transforming the relation according to the disturbance frequency and the space position

And dividing the obtained frequency domain signal into a high frequency band and a low frequency band by taking the condition that r/x is more than or equal to Kp as a condition, wherein omega is the signal frequency, Kp is a preset segmentation threshold, and the acquisition time is determined according to the frequency band length of the high frequency band.

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